The diagram on the right shows a square with side length $2\text{m}$ and lines drawn to its sides from its centre $O$. The points $A$, $B$, $C$ and $D$ are all on different sides of the square.
The lines $OA$ and $OB$ are perpendicular, as are $OC$ and $OD$.
What is the shaded area?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.